Topic: Motion in A Plane (Test 2)



Topic: Motion in A Plane
Q.1
We can define the difference of two vectors A and B as the
A. sum of two vectors A and B' such that B' is equal to B multiplied by -1
B. sum of two vectors A and B' such that B' is equal to B multiplied by -2
C. sum of two vectors A and B' such that B' is equal to B multiplied by 1
D. sum of two vectors A and B' such that B' is equal to B multiplied by 0
Answer : Option A
Explaination / Solution:

Vector subtraction is defined in the following way.

  • The difference of two vectors, A - B , is a vector C that is, C = A - B
  • The addition of two vector such that C = A + (-B). B has been taken in opposite direction.

Thus vector subtraction can be represented as a vector addition.


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Q.2
An arbitrary vector v can be expressed as
A. a sum of three mutually perpendicular unit vectors each multiplied by the same scalar constant
B. a sum of three mutually perpendicular unit vectors each multiplied by a some scalar constant
C. a sum of three mutually perpendicular unit vectors each multiplied scalar constant equal to 1
D. a sum of three mutually perpendicular unit vectors each multiplied scalar constant equal to -1
Answer : Option B
Explaination / Solution:

Set of elements (vectors) in a vector space is called a basis, or a set of basis vectors, if the vectors are linearly independent and every vector in the vector space is a linear combination of this set.In more general terms, a basis is a linearly independent spanning set.

Given a basis of a vector space, every element of vector space can be expressed uniquely as a linear combination of basis vectors, whose coefficients are referred to as vector coordinates or components.

We can represent vector v as


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Q.3
A unit vector is a vector
A. having a magnitude of 1 and points in z-direction
B. having a magnitude of 1 and points in x-direction
C. having a magnitude of 1 and points in y-direction
D. having a magnitude of 1 and points in any chosen direction
Answer : Option D
Explaination / Solution:

A unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat":  (pronounced "i-hat"). The term direction vector is used to describe a unit vector being used to represent spatial direction.

a unit vector directed along the positive x axis

= a unit vector directed along the positive y axis

 = a unit vector directed along the positive z axis


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Q.4

An arbitrary vector  in a plane can be expressed in terms of its x and y components by the equation

A. A⃗ =Axi^+Ayj
B.

C. A⃗ =Axi^Ayj
D. A⃗ =AxAy
Answer : Option A
Explaination / Solution:

In a two-dimensional coordinate system, any vector can be broken into x -component and y -component.

Vector  can be represented as 


Where  is component in direction of x-axis and  is a unit vector in same direction of x-axis 

And  is component in direction of y-axis and  is a unit vector in same direction of y-axis 

 


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Q.5

If are components of vectors A and B along the x and y axis then the sum of the vectors A and B has a component in the x direction equal to


A.

AxBx


B.           
Ax+Bx
        


  
C. Ax+Bx
D. AxBx
Answer : Option B
Explaination / Solution:

The component method of addition can be summarized this way: 

  • Using trigonometry, find the x-component and the y-component for each vector.
  • Add up both x-components, (one from each vector), to get the x-component of the total.
  • Add up both y-components, (one from each vector), to get the y-component of the total.
  • Add the x-component of the total to the y-component of the total, and then use the Pythagorean theorem and trigonometry to get the size and direction of the total.

Using these points in mind, the sum of the vectors A and B has a component in the x direction  


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Q.6
if particles A and B are moving with velocities  and  (each with respect to some common frame of reference, say ground.). Then, velocity of particle A relative to that of B is:
A.  =  + 
B.  =  - 
C.  = -  - 
D.  = -  + 
Answer : Option B
Explaination / Solution:

The relative velocity of an object A with respect to another object B is the velocity that object A would appear to have to an observer situated on object B moving along with it.

In simple words relative velocity of A with respect to Be is the vector difference between the velocities of A and B.

It is represented as 


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Q.7
The path of a projectile is
A. straight line
B. cubic
C. hyperbola
D. a parabola
Answer : Option D
Explaination / Solution:

A particle with a vertical and horizontal velocity travelling in a gravitational field will trace out a parabola.

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Q.8
Centripetal acceleration of a particle moving in a circular path with constant velocity v is given by
A.  where R is the radius of the circle
B.  where R is the radius of the circle
C.  where R is the radius of the circle
D.  where R is the radius of the circle
Answer : Option D
Explaination / Solution:

A body that moves in a circular motion (of radius R) at constant speed (v) is always being accelerated. The acceleration is at right angles to the direction of motion (towards the center of the circle) and of magnitude  
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Q.9
Which of the following physical quantities a vector?
A. mass
B. angular momentum
C. speed
D. volume
Answer : Option B
Explaination / Solution:

Angular momentum is a vector quantity (more precisely, a pseudovector) that represents the product of a body's rotational inertia and rotational velocity about a particular axis.

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Q.10
Which of the following physical quantities a scalar?
A. velocity
B. force
C. electric field
D. work
Answer : Option D
Explaination / Solution:

Work is defined as a dot-product (or scalar product) of force and displacement, both of which are vectors. A scalar (dot) product of two vectors gives a scalar result.

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